It depends on the specific child theme you’re using. We’ve had good results with WPTouch, http://wordpress.org/extend/plugins/wptouch/ …just not in every case.
Touch offers pretty good support. I recommend buying a license if the free version gets you close, but not all the way,
It’s a lifetime license, so even if it doesn’t work on the current site you’ll likely get your money’s worth sooner or later